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    Compass correction using sunrise
    From: Francois Tremblay
    Date: 2022 Jun 26, 10:43 -0700

    Hello all,

    I am relatively new to celestial navigation but very much deep into it. As an engineer, I make a point in making sure that all my calculations are precise. So far everything has worked out very nicely. But I’m now challenged by a mathematical error that I can’t figure out. It might just be the precision of the tables versus mathematical calculation. I would appreciate your input on it.

    Here’s the problem.

    I want to get the azimuth of the sun at sunrise at a specific position in the Northern Atlantic to verify the error of my compass.

    Date: June 16th, 2022

    My position: N 48° 17.0’ W 062° 28.0’.

    At this position, the sun will rise at exactly 8h08 TU (3h58 + 4)

    N 50°

    03 50

    N 48° 17.5

    03 58

    N 45°

    04 13

    Option 1. Using HO-249 the same way I do for any other sightings.

    I enter the table with DEC N 23° 23.0 / Latitude N 48° / LHA 239°. The azimuth is 052°, which makes sense.

    Option 2. Using Bowditch Tables

    I enter the table with DEC 23° and Latitude 48°. The azimuth is 054.3°. It also makes sense.

    Option 3. Finally, I use the amplitude formula instead of the Bowditch table

    A°= arcsin (sin DEC / cos a-Lat)

    A°= arcsin (sin 23° 23.0’ / cos 48° 17’)

    A°= arcsin (sin 23.383° / cos 48.283°)

    A°= 36.6°

    Z = 090 – 36.6° = 53.4°

    Here’s my question: The three results make sense but are slightly different (052°, 054.3° and 053.4°). Is it only due to the precision of the tables or is there something I forget to consider. Also, when using the first method, while the azimut (052°) seems to make sense, I get a Hc of  -1° 15’. It seems to me that Hc should be very close to 0°

    Thanks for your input!

    Francois

       
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